Simplify to lowest terms. $\dfrac{40}{56}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 56? $40 = 2\cdot2\cdot2\cdot5$ $56 = 2\cdot2\cdot2\cdot7$ $\mbox{GCD}(40, 56) = 2\cdot2\cdot2 = 8$ $\dfrac{40}{56} = \dfrac{5 \cdot 8}{ 7\cdot 8}$ $\hphantom{\dfrac{40}{56}} = \dfrac{5}{7} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{40}{56}} = \dfrac{5}{7} \cdot 1$ $\hphantom{\dfrac{40}{56}} = \dfrac{5}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{56}= \dfrac{2\cdot20}{2\cdot28}= \dfrac{2\cdot 2\cdot10}{2\cdot 2\cdot14}= \dfrac{2\cdot 2\cdot 2\cdot5}{2\cdot 2\cdot 2\cdot7}= \dfrac{5}{7}$